Answer: The mathematical expectation of Option A is 2.25. The mathematical expectation of Option B is 2.75. Option B offers a greater likelihood of advancing to the finish line.
Step-by-step explanation: I took the test.
The mathematical expectation of Option A is 1. The mathematical expectation of Option B is 1.5. Option B offers a greater likelihood of advancing to the finish line.
The mathematical expectation of a particular random phenomenon basically means the average value of the random phenomenon.
according to question
Two number cubes are rolled to determine how a token moves on a game board. The sides of each number cube are numbered 1, 2, 3, 4, 5 and 6.
Therefore, there will be 36 outcomes in total .
Product Table
1 2 3 4 5 6
1 1/2 even
2 all even
3 1/2 even
4 all even
5 1/2 even
6 all even
in which even's are
3(3) + 3(6) = 27
in total of 36 outcomes = 27/30 are even
in which odd's are
= 36-27 =9
in total of 36 outcomes = 27/30 are even
As per options given
Option A: If the product is even, move forward 4 spaces. Otherwise, move backward 8.
(4)(27/36) - 8 ( 9/36)
= 3 - 2
= 1
Option B: If the product is even, move forward 5 spaces. Otherwise, move backward 9.
(5/)(27/36) - 9( 9/36)
= 15/4 - 9/4
= 6/4
= 3/2
= 1.5
Hence, the mathematical expectation of option A = 1 option B = 1.5 and B offers a great likelihood of advancing to finish line .
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